# Inequalities Quiz Set 012

### Question 1

In a certain language different symbols represent different operators as follows.

1. ∩ means X = Y
2. ¢ means X ≯ (not more than) Y
3. @ means X ≮ (not less than) Y
4. £ means X < Y
5. \$ means X > Y

Statements: F £ G; G ∩ H; H ¢ I;

Conclusions:

1. F \$ I
2. G \$ I
A

both I and II are true.

B

only conclusion II is true.

C

only conclusion I is true.

D

neither I nor II is true.

Soln.
Ans: d

The statements can be translated to F < G = H ≤ I. Conclusion I translates to F > I. Conclusion II translates to G > I. So we can see that neither I nor II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 2

In a certain language different symbols represent different operators as follows.

1. ¥ means X = Y
2. ∧ means X ≯ (not more than) Y
3. η means X ≥ Y
4. Ξ means X < Y
5. Γ means X > Y

Statements: B Ξ C; C Ξ D; D ∧ E;

Conclusions:

1. B Γ E
2. D Ξ B
A

both I and II are true.

B

only conclusion II is true.

C

only conclusion I is true.

D

neither I nor II is true.

Soln.
Ans: d

The statements can be translated to B < C < D ≤ E. Conclusion I translates to B > E. Conclusion II translates to D < B. So we can see that neither I nor II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 3

In a certain language different symbols represent different operators as follows.

1. © means X = Y
2. ∑ means X ≯ (not more than) Y
3. Γ means X ≮ (not less than) Y
4. ∧ means X < Y
5. ∀ means X > Y

Statements: O Γ P; P ∧ Q; Q © R;

Conclusions:

1. P ∧ R
A

both I and II are true.

B

only conclusion II is true.

C

only conclusion I is true.

D

either I or II can be true.

Soln.
Ans: a

The statements can be translated to O ≥ P < Q = R. Conclusion I translates to P < R. Conclusion II translates to Q = R. So we can see that both I and II are true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 4

In a certain language different symbols represent different operators as follows.

1. ¢ means X = Y
2. ® means X ≤ Y
3. ¥ means X ≥ Y
4. ∅ means X < Y
5. ⊗ means X > Y

Statements: T ¢ U; U ∅ V; V ∅ W; W ⊗ X;

Conclusions:

1. U ∅ X
2. T ∅ X
3. W ⊗ T

Which of the above conclusions is/are true?

A

III only.

B

both III and II.

C

II only.

D

I only.

Soln.
Ans: a

The statements can be translated to T = U < V < W > X.

The conclusions translate to:

1. U < X(False)
2. T < X(False)
3. W > T(True)

### Question 5

In a certain language different symbols represent different operators as follows.

1. £ means X = Y
2. ⊗ means X ≤ Y
3. ∀ means X ≥ Y
4. ∏ means X < Y
5. Ξ means X > Y

Statements: B £ C; C £ D; D Ξ E;

Conclusions:

1. B £ E
2. C Ξ E
A

both I and II are true.

B

only conclusion II is true.

C

only conclusion I is true.

D

either I or II can be true.

Soln.
Ans: b

The statements can be translated to B = C = D > E. Conclusion I translates to B = E. Conclusion II translates to C > E. So we can see that only conclusion II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥. 